Visualising relativistic effects in redshift space distortions of large scale structure

Abstract: Observing large scale structure in redshift space gives rise to the well known redshift space distortions whereby a spherical distribution of galaxies is distorted into an ellipsoid along the line of sight of the observer. This effect is important on linear scales and so can be thought of as a Newtonian correction to the density perturbation even though their physical origin is in the Doppler effect. On larger scales subtler aspects of the Doppler and gravitational redshift effects give rise to further distortions in redshift space. These further contort objects beyond an ellipsoidal compression, into shapes with broken line-of-sight symmetry such as an egg- or bean-like shapes. In this paper, we aim to qualitatively picture how large over-dense regions, including clusters or superclusters, and under-dense regions, such as voids, undergoing infall or outflow respectively, become distorted in redshift space when higher-order relativistic effects are taken into account. This will contribute when analysing structure in real space such as stacking voids which are no longer radially symmetric when these effects are included.